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Cheiroballistra
= Introduction = This reconstruction is mostly based on Iriarte's (2000; 2003) interpretation of the cheiroballistra, corrected where appropriate with my own amendments. When discussing the ancient texts I have had to resort to English translations provided by Marsden (1971: 206-233) and Wilkins (1995: 10-33) and comments made by Iriarte (2000; 2003) and others. I've also to a lesser extent made use of Schneider's (1906) German translation. Analysis of the archaeological finds is mostly based on the numerous publications of Baatz. In this article and reconstruction I've made a few underlying assumptions and followed a few key principles. First, Pseudo-Heron's (P.H.) Cheiroballistra text assumed to be more or less complete. No parts are assumed missing, unless it's certain that the reconstruction can't work without them. Second, the goal has been to make the reconstruction fit the text, not vice versa. This principle is followed as far as reasonably possible. For a good example of this principle, see discussion below about the tenons of the rungs in the little ladder. Most other scholars have ignored the limitations in the metalworking techniques and tools used by the Greeks and the Romans. To arrive at a realistic reconstruction, these need to be taken into account. Again, there's a good example of this in the little ladder section. = Main controversies = Outswinger or inswinger Archaeological finds strongly suggest that the cheiroballistra was an inswinger so I've reconstructed it as such. This issue has already been discussed in detail here. Winched or not winched? There is another long lasting disagreement about general mode of operation of the cheiroballistra. Some scholars (e.g. Marsden, Wilkins) have assumed the cheiroballistra was cocked with a winch. Then there are those (e.g. Baatz, Iriarte, Stevenson) who believe the cheiroballistra was cocked similarly to gastraphetes by pushing the slider back with one's bodyweight alone. It should be noted that Marsden did not have a chance to see any archaelogical remains of cheiroballistra -style ballistas before his early death. Wilkins (1995) has lots of arguments in favor of a winched cheiroballistra in both of his JRMES articles (1995; 2000). First, he states that the cheiroballistra had the same spring diameter as old wooden-framed one-cubit or two-span ballistas and thus had to be cocked with a winch (1995: 39; 2000: 96). However, as Iriarte (2000: 57) points out, both Wilkins (1995: 21) and Marsden (1971: 223-224) increased the inner diameter of the washers given in text (2 dactyls). This quickly led both into problems, the most immediate one being the inadequate length of the levers resting on top of the washers. If the spring diameter is enlarged, the levers - in text 3 dactyls long - would no longer protrude from the washers enough and tightening the spring bundles with a spanner would be impossible. Therefore Wilkins (1995: 24) had to lengthen the levers to 3,5d. Marsden (1971: 222) with his more conservative increase of washer diamater did not strictly have to do that - end result being that his levers did not protude from the washers and as such did not fulfill their purpose. Second, Wilkins (1995: 39; 2000: 94) clearly assumes all pre-cheiroballistra ballistas had winches. This idea is almost entirely based on two statements given by Heron in his Belopoeica (e.g. Marsden 1971: 21, 25). However, as is clear from Marsden's translations Heron is simply describing what the engineers had to do to be able create even stronger ballistas. No amount of text analysis will ever make Heron say that less powerful ballistas cocked in gastraphetes-style (Marsden 1971: 23) were discontinued or that torsion springs themselves - whatever their size - were too powerful to be cocked manually. It is clear that Wilkins places way too much faith in his interpretation of the statements made by an ancient author he considers "authoritative" (Wilkins 2000: 94, 99). Another argument in favor of a winched cheiroballistra is it's weight, as Wilkins (1995: 39) points out. The machine can't be too heavy, or the advantages of winchless operation are lost. Another related issue is the centre of gravity of the machine. According to Wilkins Digby Stevenson has reconstructed a gastraphetes-style cheiroballistra which weighed ~12 kilograms (Wilkins 1995: 39; 2000: 97). Iriarte's reconstruction weighs only 9 kilograms (Iriarte 2000: 65). Most of the weigh of the machine comes from the metal parts - or parts thought to be made of metal. As many dimensions of these parts are missing, reconstructions will be highly subjective and will be based on the assumed strain levels the machine. Therefore the weight of winched cheiroballistras cannot be taken as proof against the stomach bow theory. Wilkins also argues - not very convincingly - that because the material for the handle (part of the triggering mechanism at the end of the slider) was said to be of iron, it should be taken as a further proof that cheiroballistra was winched (Wilkins 1995: 16). He argues that usually P.H. did not state which material to use, so unless considerable strain was placed on the handle, other material such as bronze should have been perfectly satisfactory and no mention of iron would have been necessary. This does not make much sense to me, as the material for the little ladder and it's rungs and cross-piece are not given, either, and these are under considerable stress, too (see Marsden 1971: 214-217; Wilkins 1995: 27-28). Also, the weakest link in the handle and slider construction is the wooden slider, not the handle. This is because the handle is attached to the end of the slider and - as we know - wood splits very easily. Wilkins (1995: 16) noticed this and realized that the end of the slider had to be reinforced with metal plating. Finally, as Iriarte (2000: 57) points out, there is archaeological evidence of small ~2 dactyl washers from Ephyra and Elginhaugh. This proves that small ballistas were in fact used. There are basically two ways to discredit these finds. First, one can argue that this kind of small washers were never used widely and these are just isolated cases. This is, however, unlikely due to how archaeological record is formed. Archaeological finds consist almost exclusively of abandoned and/or lost items. In addition, only a small fraction of the items that were lost or abandoned ever reach the archaeological record for a variety of reasons. So, unless were talking of a closed find such as a city overrun by volcanic ashes or covered by a landslide - or perhaps a shipwreck - we're most likely going to encounter common items of little monetary or reuse value. This means it's likely that small washers were common, not rare, and we're going to find lots of them in the future. The second counterargument is that the washers belonged to "toys", not real weapons. Whether they were toys did not depend on the washer diameter but the performance (as defined here) of the ballistas they belonged to. In a nutshell there is no reason to forcefully interpret the cheiroballistra text to describe a winched weapon or to try discrediting the stomach-bow theory as Wilkins (1995: 38-41; 2000: 94-100) does. Power and performance I found it necessary to write this section because Wilkins seems to consistently confuse power with performance. In this article power refers to either power fed into the system (ballista) or the kinetic energy of the projectile. Performance, on the other hand, refers to the weapon's usability and effectiveness in conflict situations (sieges, battlefield etc.). Wilkins (2000: 94, 96) argues that stomach-bow proponents are not taking into account the "performance requirements" of ancient catapults. Being a winch proponents what he really meant to say is "power requirements". He does not take into account the performance of the weapon as defined here. What is clear, however, is that the cheiroballistra had to be somehow superior to handbows and other missile weapons of the era to make any sense. Unlike Wilkins seems to think, power is only small part of the equation. Other factors include things like cost of manufacture, ammunition and training, as well as power, accuracy, range, initial velocity and weight of ammunition. One key factor is also the efficiency of energy transfer, meaning how much of the energy put into the torsion springs is transmitted into the bolt as kinetic energy. Being superior to contemporary missile weapons even in one or few of these areas might be enough to justify use of relatively low-powered hand-cocked weapon. Cheiroballistra's only undisputed disadvantages compared to the handbow is it's weight and somewhat slower rate of fire. Cost might be another, but complex handbows made from sinew, wood and horn were not cheap, either. Also, unlike Wilkins (2000: 96) thinks, the weight of the ballista bolt has little to do with it's performance as a weapon. He argues that light bolts (as in 25 or 42 grams) would be useless in war. This is the case only if the bolt's speed is very low similarly to those in Wilkins' own reconstructions (Wilkins 2000: 93): * Winched cheiroballistra: 47m/s with 100 gram bolt (110 joules). Apparently the pull was around 739 pounds as in Wilkins' earlier tests. * Winched three-span ballista: 37m/s with 200 gram bolt (136 joules). These are not especially impressive results given the amount of energy fed into the system. As a comparison a few tests from the author and Tim Baker who has done extensive research on performance of traditional handbows: * From Baker (2000: 114-115), all bows drawn 28 inches: ** Average 40 lbs all-wood, straight handbow: 42,09 m/s avg using a 32,5 gram arrow (29 joules) ** Average 50 lbs all-wood, straight handbow: 45,75 m/s avg using a 32,5 gram arrow (34 joules) ** Average 60 lbs all-wood, straight handbow: 49,72 m/s avg using a 32,5 gram arrow (40 joules) ** Average 70 lbs all-wood, straight handbow: 53,99 m/s avg using a 32,5 gram arrow (47 joules) * Author's ~150 lbs crossbow with steel bow: ** 55,7 m/s avg using a 28 gram bolt (44 joules) ** 47,7 m/s avg using a 50 gram bolt (56 joules) * Author's ~300 lbs crossbow with steel bow: ** 54,4 m/s avg using a 52 gram bolt (77 joules) ** 46,5 m/s avg using a 81 gram bolt (88 joules) Note that due to the shorter power stroke crossbows need to have draw weight 2-3 times higher than handbows to achieve same energy storage levels. Because of it's thicker bow the 300lbs crossbow has a much shorter draw than the 150lbs crossbow. If it had been scaled up by increasing size of all parts and hence it's draw length, it would have matched or exceeded Wilkins' ballistas' performance. The heavier weight handbows could use heavier arrows to increase kinetic energy of the arrows. The weaker bows are already operating at high efficiency levels. Handbows used for war pulled 100lbs and more (***reference***), so the kinetic energy of their arrows is pretty close to those of Wilkins cheiroballistra bolts. It seems clear that efficiency (as defined above) of Wilkins' reconstruction is very bad. As weapons of war they would have been nearly useless due to their weight, slow rate of fire and poor range. Light bolts from a properly designed ballista would have been effective, as long as the velocity was high enough. There is evidence that a properly designed Orsova ballista reconstruction with inswinging arms can consistently reach velocities of 90 m/s with ~400 gram ammunition and 5000 pound draw weight. As of 3th August 2010 this reconstruction has not yet even reached it full potential, but still the velocity is nearly twice as high as in Wilkins' cheiroballistra. There is no reason to think that velocity would be significantly reduced by scaling down the machine, as long as bolt weight is scaled down, too. According to Wilkins (2000: 97), the average stomach pressure of a man is around 68 kg. Although the draw weight of an inswinger (see below) does not increase linearly (as with an outswinger, see below), we can still arrive at some very rough figures for the kinetic energy of the bolt. As 90m/s is clearly doable for an inswinger, we can use that as a starting point. The handbows in above list have 28 inch (71,12 cm) draw length. The cheiroballistra has a draw length of 27,36 dactyls (54,17 cm), or around 77% of handbow draw length. This means that at any given draw weight the cheiroballistra stores only 77% of the handbow's energy. Now, as Wilkins (2000: 97) approximated, gastraphetes-style cheiroballistra's draw weight is around 68kg (or ~150 international pounds). So the cheiroballistra stores the same amount of energy as a 115 pound handbow (150*0,77), which is between 70-80 joules. At 90m/s this translates to bolt weighing between 19,7 and 22,2 grams. Of course all this is speculation until real tests with a small gastraphetes-style cheiroballistra materialize. However, if 90m/s + velocities are obtainable with cheiroballistras cocked by hand they have three main benefits compared to handbows: * More kinetic energy * Significantly improved range * Better penetration due to smaller cross-section of the bolt Many scholars have used archaeological finds of bolts or boltsheads as basis for their ballista missile reconstruction (e.g. Iriarte 2000: 66-68; Wilkins 1995: 45; Wilkins 2000: 95-96). This is dangerous because it tends to limit testing to random bolts originally belonging to random ballistas (or even crossbows). This almost certainly gives false impression of a ballista's capabilities such as range and power. The problem should approached the other way around, by rigorously testing different bolt weights to find the best match between kinetic energy and initial velocity for each individual ballista. If too light bolt is used, the arms have lots of energy left at the end. On the other hand, if too heavy bolt is used, the ballista will transfer energy efficiently into the bolt, but the initial velocity and range of the bolt may be disappointing. = Cheiroballistra parts = Conventions All measurements are in Greek dactyls (1,93cm). Measurements which are derivable from the text are marked in green. Measurements which are subjective and not given in text are marked in red. Case The case is the lower part of the cheiroballistra stock with a female dovetail groove running down it's length. The upper part of the stock, slider, has the male dovetail which allows it to slide on top of the case. Although the description of the case (e.g. Marsden 1971: 213) is relatively clear compared to most other sections in Heron's cheiroballistra, it can still be interpreted in a number of ways. The part describing the location of the projecting block (ΚΘ) is corrupt in all manuscripts and does not make sense as is. A simple solution to this corruption was suggested first by Prou's (1877: 120-121) and later Iriarte's (2000: 48). Both simply substituted ΑΘ with ΛΘ and the text makes perfect sense. While this theory sounds most plausible to me, other explanations have been suggested by Marsden (1971: 218), Wilkins (1995: 11-12), Schneider (1906: 149) and Baatz (1974: 70). The actual purpose of the projecting block has confused pretty much every researcher, as Iriarte (2000: 48) points out. I have interpreted it simply as a support for the little ladder holding the field frames. This is the simplest solution to keep the little ladder, the field frames and the little arch from moving backwards when the weapon is cocked. Of course, some additional ironwork is needed, but much less than without support from the projecting block. As Wilkins (1995: 12) notes, removing wood along ΛΘ and ΑΚ as suggested by Heron (e.g. Marsden 1971: 213) seems silly. It seems clear that Heron is not thinking like a carpenter, who would have simply glued or nailed a piece of wood to bottom of the board ΑΒ and be done with it - as did I. Full CAD drawing of the case below: Slider The slider has a male dovetail corresponding to the female dovetail in the case. Although a relatively simple component, it's exact form is still not clear. There are two competing interpretations for the slider's cross-section: * Most scholars (e.g. Marsden 1971: 218, Wilkins 1995: 11) have reconstructed the slider from two pieces forming a "T" shape. The lower part of this composite construction was the male dovetail to which the upper part was attached. The upper part simply rests on top of the case. * Iriarte (2000: 52) suggests that the slider was made from one piece. These differing interpretations stem from the fact that Heron did not state how wide the female dovetail should be; he only gives it's depth (1d) and length (46d). He also says that the slider should be "about" 2,5d wide and 1,25d high. The "T" proponents take 2,5d to mean the width of the upper (non-dovetail) part of the slider, whereas Iriarte (2000: 52) suggests that the male dovetail itself - being the only part of the slider - was about 2,5d wide. I've personally followed Iriarte's interpretation as it is simpler and requires one to make fewer questionable assumptions. The "about" (see Iriarte 2000: 52) in slider width requires some discussion. If the slider was 2,5d wide, then only 0,5d (or ~1cm) of wood would be left on both sides of the slider. This is not much, but might be enough for durable operation. Nevertheless, I've made the slider slightly narrower (2d). Crescent-shaped piece Little ladder The actual description of the actual little ladder (ΛΜΝΞΟΠΡΣ) is relatively clear (e.g. Marsden 1971: 215-216; Wilkins 1995: 26-29). Only the part describing the tenons (ΛB, ΝΓ, ΟΔ, ΡΕ) is very vague and further evidence has to be sought for from archaeological finds. It is highly likely that the tenon parts of the little ladder were similar to those in the Orsova kamarion (Baatz 1978: 11). The lower surface of the boards ΛΜΝΞ and ΟΠΡΣ was probably curved, as Wilkins (1995: 29) notes. The thickness of the boards themselves is not given. Several scholars have arrived at widely different translations or interpretations of the same section of the text: Marsden (1971: 215), referring to the beams (ΛΜΝΞ and ΟΠΡΣ): The thickness each is to be 0,5d, and the length? of each of the tenons ... is to be 2d Wilkins (1995: 28): Let the thickness of each of the Tenons ... be 1/2 dactyl. Iriarte (2000: 57): The thickness of each one of the tenons ... must be 2 d. Marsden's 0,5d for the thickness of the board is completely arbitrary addition. Again, the lack of thickness figure allows anyone to make the little ladder just as strong as is required. The material for the boards is usually assumed to be iron. In case the boards were made of iron, 0,5 d (~1cm) as suggested by Marsden is way too strong (and heavy) for a gastraphetes-style weapon. A more realistic figure would be 0,17 dactyls (~0,35cm). Although the cheiroballistra text is apparently describing boards made of iron, hardwood could be used instead: 0,75d thick boards should be strong enough. In any case, the boards had rectangular holes at Τ and Υ and round holes at Φ, Χ, Ψ and Ω. Each board had three holes which were the same distance (=equidistant) from each other. Although not clearly stated, the distance between the ends of the boards and the outermost holes should almost certainly be the same. Both Marsden (1971: 225) and Wilkins (1995: 29) apparently misinterpreted this part of the text, placing the round holes at the same distance from the center on both boards. This meant that without an extra pair of holes the rungs would rotate. The correct way is to treat both boards separately and not just copy the locations for holes from one beam to the other. As the boards are of different length, the holes do not coincide, which prevents the rungs from rotating as suggested by Iriarte (2000: 58). In fact, I had reached the same conclusion before reading Iriarte's article. Similarly, the hole in the middle is rectangular to prevent the cross-piece from rotating. The crosspiece (ΤΥ) and rungs (ΦΧ and ΨΩ) are placed between the two boards (ΛΜΝΞ and ΟΠΡΣ) as spacers. All of the are told to be 3d long (not counting the tenons) and 2,5d wide. The thickness is not given, which leaves open many interpretations. Most well-known scholars have made the crosspiece and rungs from thick iron plate. If we assume that the crosspiece and rungs were made from iron, there were only two practical ways to make them with tools and techniques of that time: * Forging the crosspieces, rungs and their tenons from the same piece of iron. This requires forging a flat iron plate and then chiseling away excess material from around the tenons. After this the tenons of the rungs have to be forged round. This last step is entirely unnecessary, as the holes in the boards had to be punched anyways and punching round and rectangular holes is as easy. Regardless, this whole process would have been relatively fast. * Welding the tenons to the crosspieces and rungs. This technique does not waste material, but involves lots of welding of small pieces of iron. As each tenon and it's corresponding crosspiece or rung had to be heated to welding heat together, the risk of melting the crosspiece or the rungs was high. The process would have been pretty slow and would have consumed lots of charcoal: therefore this technique seems unlikely. Some modern reconstruction are made by boring holes through the rungs and inserting tenons through them (e.g. Wilkins 1995: 28). This was not feasible in antiquity, where the only realistic method of making holes to thick pieces of irons was punching. While punching through the beams - even very thick ones - is trivial, punching a hole accurately through a relatively narrow but 3d (~6cm) thick piece of steel is not an option. Other modern reconstructors don't clearly state how their crosspieces and rungs are made (e.g. Iriarte 2000: 58; Marsden 1971: 225). And alternative explanation is that instead of iron cross-piece and rungs wooden spacers were used. They could have been the same height as the boards. According to Marsden (1971: 217) P.H. states that the cross-piece was riveted. Wilkins (1995: 28) uses the term "to pin" instead of "to rivet". In any case, there's no talk of riveting (or pinning) the round tenons of the rungs. This would imply that they were left loose and in fact, there's no need to attach them securely: the ends of the boards are securely held together by the metal hoops of the field frames and the middle by the rectangular rivet going through the cross-piece. This allows both the cross-piece and the rungs to be made of wood without any difficulty, their only metal component being the rectangular iron rivet going through the crosspiece and beams. The wooden spacers would be trivial to make, much lighter than their iron counterparts and would even support the little ladder better because of their greater height. The rungs would have had round holes to which round wooden (or iron) tenons were inserted. Field frames Field frames are spring-frames used to house the spring cord. Wescher's (1867) edition of the cheiroballistra does not unfortunately include pictures of these bars. Fortunately Schneider's edition (1906: 154) does. However, best illustrations are in Wilkins' edition (1995: 18). In addition, there are several archaeological finds of field-frames. There are two field frames in each cheiroballistra, each consisting of one curved bar (ΔΒ and ΗΘ) and one straight bar (ΑΓ and ΕΖ). To the end of these bars two rings are attached at ΚΛ, ΜΝ, ΞΟ and ΠΡ. In codex M's diagram (see Wilkins 1995: 18) the Ζ is clearly in the wrong place - it should be next to Π. This does not affect the interpretation in any way, though. Below is an image of the field-frame bars: The characteristic curve in the middle of outer bars is formed by bending the thicker side of the bar. This method was used on some of the archaeologically attested field-frames, namely in Orsova and Lyon artefacts. This makes sense, as it does not make the curved bar too weak to withstand the pressure of the torsion springs. In Gornea field-frames the curved bar was bent along it's thinner side. However, the curved part of the bar was significantly widened, almost certainly to prevent the pressure of the spring cord from bending it. The curve in Gornea field-frames also seemed to be more modest than that in Orsova and Lyon field-frames. The Sala field-frame was cast from broze and it follows the Orsova / Lyon style. Triggering mechanism The triggering mechanism in cheiroballistra text is very vaguely described. Fortunately the manuscript diagrams (see Wescher 1867 and Schneider 1906) clarify the text a lot. Regardless, dimensions of the components are lacking; only the length of the incision in the claw is given. This reconstruction of the trigger is based on Iriarte's (2000) work. Wilkins reconstruction, though commendable, is based on the idea that cheiroballistra had a winch (1995: 14-17). Fork Similarly to the claw, all authors agree upon the general appearance of the fork (ΕΖΗΘ). Wilkins (1995: 14) calls this component double bracket and tenon. The part ΕΖ is a double bracket and ΗΘ a rectangular tenon. The double bracket is bored at ΤΥ to receive an axle. The same axle is pushed through the hole bored at Φ in the claw. The fork is sunk to the slider from it's rectangular tenon end and riveted (from below). Note that the letters in manuscript diagrams don't exactly match what we'd expect looking at the text. Claw The claw (ΚΛΜ) is well-known from older artillery pieces, so there is little disagreement on it's general form (see Marsden 1971: 219-220; Wilkins 1995: 17; Iriarte 2000: 52-53). The claw has an incision of 1 dactyl long and has a horizontal, round hole at Φ. This hole is used for the claw axle which also goes through holes in the fork. Trigger Similarly to the claw and fork the general form of the trigger (ΝΞ) is well know and agreed upon. Wilkins (1995: 14) has translated this component as the snake. A round hole is punched or bored to the trigger (from top) at Ν. A corresponding hole is bored to the slider (ΓΔ) at Π. An axle is then inserted through both holes. This allows the trigger to rotate around it's axle on top of the slider. Handle The interpretation of the handle (ΑΒΓΔ) depends on whether one reconstructs a winched weapon or not. The general form is handle is surely the same as that shown below: In the text it's stated clearly that there's a round hole at Δ, at the bottom of the handle. A corresponding hole is bored to the slider (ΓΔ) at ΜΝ. The handle and slider are then attached together with a pin/axle. Also, a rectangular hole is pierced to the slider at Ξ. The location of this second, rectangular hole is only marked into one of the manuscript diagrams - it is located just behind the round hole (ΜΝ) (see Wescher 1867: 127-128). Iriarte (2000: 52-53) interpreted the rectangular hole as a lengthwise, rectangular incision extending forward from the end of the slider. In Iriarte's reconstruction the handle rotated freely up and down, which was necessary to lock and unlock it to it's anchor (a strong nail) at the end of the draw and after release. Wilkins (1995: 16-17) placed the handle horizontally and used it as attachment point for the winch. He made the rectangular hole perpendicular to the stock, which allowed him to make the handle stronger. This suited his winched cheiroballistra scheme better. Pi bracket The Π (pi) bracket (ΟΠΡΣ) is one of the most controversial parts of the triggering mechanism. Marsden (1971: 221-222) thought it to be a rivet-plate to which other triggering mechanism parts were attached to. Gudea & Baatz (1974: 62), followed by Wilkins (1995: 16) and Iriarte (2000: 53-54) interpreted it as handgrip for pushing the slider forward. Wilkins (1995: 16) placed the pitarion in front of the fork, whereas Iriarte (2000: 53-54) placed it behind it. Either approach seems to work in practice and has little effect on the functionality of the machine - if the handgrip interpretation is correct. = Relation of the parts = Category:backup